Dissipative adaptation.
We finally investigate how dissipative adaptation underlies the self-replication in the present model.
As stated in the introduction, dissipative adaptation is a general thermodynamic mechanism explaining lifelike self-organization in classical far-from-equilibrium systems.
It clarifies how fine-tuned, exceptional behaviours can be fundamentally related with work consumption.
The main picture is that, when a given fluctuating physical system absorbs work from its environment, it can reach exceptional dynamical transformations that are selected by the work source characteristics.
If the excess energy provided by this nonequilibrium work source is dissipated to the environment (in the form of heat), the system can get irreversibly trapped in those rare configurations; in other words, adapted to its environment.
Mathematically, this idea is best described in terms of a fluctuation theorem.
By using Crooks' microscopic reversibility condition for the forward, \(p_{i\rightarrow j}(t)\) , and backward, \(p^*_{j\rightarrow i}(\tau -t)\) , classical trajectory probabilities between the initial \(i\)  and the final \(j\)  states [1]}, the dissipative adaptation has been formulated as [2]}, [3]}
\(\frac{p_{i\rightarrow j}(t) }{p_{i\rightarrow k}(t) } =e^{-\beta E_{kj}}\frac{p^*_{j\rightarrow i}(\tau -t) }{p^*_{k\rightarrow i}(\tau -t) }\frac{ \langle e^{-\beta W_{\mathrm {abs}} } \rangle _{ik}}{\langle e^{-\beta W_{\mathrm {abs}} } \rangle _{ij} },\) 
